The position of a particle of mass m = 0.8 kg as a function of time is r = x i + y j = R sin ωt i + R cos ω^t j, where R = 4.0 m, and ω = 2π s^-1. 

(a) Show that this path of the particle is a circle of radius R with its center at the origin. 

(b) Compute the velocity vector. Show that v_x/v_y = -y/x. 

(c) Compute the acceleration vector and show that it is in the radial direction and has the magnitude v₂/r. 

(d) Find the magnitude and direction of the net force acting on the particle.